University of TabrizComputational Methods for Differential Equations2345-39822320140701Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions1231393006ENMohammadShahriariUniversity of Maragheh0000-0002-8982-2451Journal Article20140222This paper deals with the boundary value problem involving the differential equation <br /> <br /> ell y:=-y''+qy=lambda y, <br /> <br /> subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions <br /> y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). <br /> <br />In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new Hilbert space and using spectral data of a kind, it is developed the Hochestadt's result based on transformation operator for inverse Sturm-Liouville problem with parameter dependent boundary and discontinuous conditions. Furthermore, it is established a formula for q(x) - tilde{q}(x) in the finite interval, where tilde{q}(x) is an analogous function with q(x).https://cmde.tabrizu.ac.ir/article_3006_b58f6612cd4666d0abfa3f6283667255.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822320140701An analytic study on the Euler-Lagrange equation arising in calculus of variations1401523007ENAbbasSaadatmandiUniversity of Kashan, Kashan, Iran0000-0002-7744-7770TaherehAbdolahi-NiasarUniversity of Kashan, Kashan, IranJournal Article20141112The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method.https://cmde.tabrizu.ac.ir/article_3007_36f175ff9db969636d2acf6818995572.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822320140701A new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics1531703267ENMehmetEkiciDepartment of Mathematics, Faculty of Science and Arts, Bozok University, Yozgat, TurkeyAbdullahSonmezogluDepartment of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, TurkeyElsayed M. E.ZayedMathematics Department, Faculty of Science, Zagazig University, Zagazig, EgyptJournal Article20141207In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity and advantages of the novel method. As a result, some new exact solutions including solitary wave solutions and periodic wave solutions are successfully obtained. The proposed approach can also be applied to other nonlinear FPDEs arising in mathematical physics.https://cmde.tabrizu.ac.ir/article_3267_6fb1541e5549a21636a8332f6f894880.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822320140701New Solutions for Singular Lane-Emden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives1711853281ENWaleed M.Abd- ElhameedDepartment of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi ArabiaYoussriYoussriDepartment of Mathematics, Faculty of Science, Cairo University, Giza-EgyptEid H.DohaDepartment of Mathematics, Faculty of Science, Cairo University, Giza-EgyptJournal Article20141210In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear Lane-Emden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the equations with their initial conditions into systems of linear or nonlinear algebraic equations which can be solved by using suitable numerical solvers. The Legendre and first and second kind Chebyshev operational matrices of derivatives can be deduced as special cases of the constructed operational matrices. For the sake of testing the validity and applicability of the suggested numerical algorithms, three illustrative examples are presented.https://cmde.tabrizu.ac.ir/article_3281_dd3a3207162ca5e8bb3b946eb9f13496.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822320140701Numerical inversion of Laplace transform via wavelet in ordinary differential equations1861943318ENCHUN-HUIHSIAONo.101, Sec. 2, Jhongcheng Rd., Shihlin District, Taipei City 111, Taiwan, R.O.C.Journal Article20150129This paper presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that $P$ is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulaes of listing table to a minimum expression and obtain the optimal operation speed. The local property of Haar wavelet is fully applied to shorten the calculation process in the task.https://cmde.tabrizu.ac.ir/article_3318_45b84a55dd6bdc7e3ffbda5bbc7be1c0.pdfUniversity of TabrizComputational Methods for Differential Equations2345-39822320140701Numerical solution for boundary value problem of fractional order with approximate Integral and derivative1952043446ENAbdol AliNeamatyDepartment of Mathematics, University of Mazandaran, Babolsar, IranBahramAgheliDepartment of Mathematics, University of Mazandaran, Babolsar, IranMohammadAdabitabarDepartment of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IranJournal Article20150129Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three numerical examples are presented to describe the fractional usefulness of the suggested method.https://cmde.tabrizu.ac.ir/article_3446_9fcbc0e8eb31a05b0a5e5b982d059e45.pdf